Let Sn = X1 + ... + Xn denote the nth partial sum of an i.i.d. sequence of random variables having positive mean [mu] and finite variance [sigma]2, and let N(s) = minlcubn [greater-or-equal, slanted] 0: Sn+1 srcub denote the corresponding renewal process. We investigate the strong limiting...

We establish the functional central limit theorem and law of the iterated logarithm for the Pickands estimator of the dependence function of a bivariate extreme-value distribution. Our methods are based on general results for sums of random variables taking values in Banach spaces.

We establish optimal approximation rates of empirical P--P and Q--Q plot processes by sequences of Brownian bridges.

Let Fn and Gn denote the Kaplan-Meier product-limit estimators of lifetime distributions based on two independent samples, and let Fninv and Gninv denote their quantile functions. We consider the corresponding P-P plot Fn(Gninv) and Q-Q plot Fninv(Gn), and establish strong approximations of...

A new model for point processes is developed which assumes that the interarrival times are exponentially distributed and follow joint multivariate extreme value distributions. It is shown that such processes may arise via natural generating procedures, and that, under very weak assumptions, that...

This paper concerns an asymptotic expansion for the distribution of the sum of independent zero-one random variables in case where this surn has variance [sigma]n2 -- [infinity]. The expansion presented is given to the order O([sigma]n-2). An application to the study of the exact rate of...

The processes of the form , where K is a constant, and B(·) a Brownian bridge, are investigated. We show that and are both Brownian bridges, and establish the independence of and , this implying that the law of coincides with the conditional law of B, given that . We provide the...

Motivated by asymptotic problems in the theory of empirical processes, and specifically by tests of independence, we study the law of quadratic functionals of the (weighted) Brownian sheet and of the bivariate Brownian bridge on [0,1]2. In particular: (i) we use Fubini-type techniques to...

Let {[alpha]n(t),0[less-than-or-equals, slant]t[less-than-or-equals, slant]1} and {[beta]n(t),0[less-than-or-equals, slant]t[less-than-or-equals, slant]1} be the empirical and quantile processes generated by the first n observations from an i.i.d. sequence of random variables with a uniform...